{"product_id":"theta-functions-von-jun-ichi-igusa","title":"Theta Functions","description":"\u003cp\u003eThe theory of theta functions has a long history; for this, we refer A. Krazer and W. Wirtinger the reader to an encyclopedia article by (\"Sources\" [9]). We shall restrict ourselves to postwar, i. e. , after 1945, periods. Around 1948\/49, F. Conforto, c. L. Siegel, A. Well reconsidered the main existence theorems of theta functions and found natural proofs for them. These are contained in Conforto: Abelsche Funktionen und algebraische Geometrie, Springer (1956); Siegel: Analytic functions of several complex variables, Lect. Notes, I. A. S. (1948\/49); Well: Theoremes fondamentaux de la theorie des fonctions theta, Sem. Bourbaki, No. 16 (1949). The complete account of Weil's method appeared in his book of 1958 [20]. The next important achievement was the theory of compacti­ fication of the quotient variety of Siegel's upper-half space by a modular group. There are many ways to compactify the quotient variety; we are talking about what might be called a standard compactification. Such a compactification was obtained first as a Hausdorff space by I. Satake in \"On the compactification of the Siegel space\", J. Ind. Math. Soc. 20, 259-281 (1956), and as a normal projective variety by W. L. Baily in 1958 [1]. In 1957\/58, H. Cartan took up this theory in his seminar [3]; it was shown that the graded ring of modular forms relative to the given modular group is a normal integral domain which is finitely generated over C.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783642653179\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783642653179","offer_id":39437884358749,"sku":"9783642653179","price":128.39,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/2cb63f48-5de5-485b-82b4-3080766fb9f5.jpg?v=1772173402","url":"https:\/\/shop.autorenwelt.de\/en\/products\/theta-functions-von-jun-ichi-igusa","provider":"Autorenwelt Shop","version":"1.0","type":"link"}